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Effort Allocations in Elimination Tournaments

Author

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  • Aner Sela

    (BGU)

Abstract
We study elimination tournaments with n stages and 2n symmetric players. The players have effort budgets that decrease within the stages proportionally to the efforts allocated in the previous stages such that for each effort unit that a player allocates, he loses α (the fatigue parameter) units of effort from his budget. We show that if the fatigue parameter α is larger than 1n−t+1, the players allocate their efforts equally over all the first t stages, t≤n−1. In particular, if the fatigue parameter α is larger than 12, the players allocate their efforts equally over all the first n−1 stages, and only in the final stage, they exert a lower effort.
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Suggested Citation

  • Aner Sela, 2021. "Effort Allocations in Elimination Tournaments," Working Papers 2103, Ben-Gurion University of the Negev, Department of Economics.
    • Handle: RePEc:bgu:wpaper:2103
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    References listed on IDEAS

    as
    1. Matthias Kräkel, 2014. "Optimal seedings in elimination tournaments revisited," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(1), pages 77-91, April.
    2. Aner Sela & Eyal Erez, 2013. "Dynamic contests with resource constraints," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 863-882, October.
    3. Rosen, Sherwin, 1986. "Prizes and Incentives in Elimination Tournaments," American Economic Review, American Economic Association, vol. 76(4), pages 701-715, September.
    4. Stracke, Rudi & Höchtl, Wolfgang & Kerschbamer, Rudolf & Sunde, Uwe, 2014. "Optimal prizes in dynamic elimination contests: Theory and experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 102(C), pages 43-58.
    5. Netanel Nissim & Aner Sela, 2020. "The Third Place Game," Journal of Sports Economics, , vol. 21(1), pages 64-86, January.
    6. Dmitry Ryvkin, 2009. "Tournaments of Weakly Heterogeneous Players," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 11(5), pages 819-855, October.
    7. Dmitry Ryvkin, 2011. "Fatigue in Dynamic Tournaments," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 20(4), pages 1011-1041, December.
    8. Christian Groh & Benny Moldovanu & Aner Sela & Uwe Sunde, 2012. "Optimal seedings in elimination tournaments," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 49(1), pages 59-80, January.
    9. Mark Gradstein & Kai A. Konrad, 1999. "Orchestrating Rent Seeking Contests," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 571-580, Springer.
    10. Jeff Horen & Raymond Riezman, 1985. "Comparing Draws for Single Elimination Tournaments," Operations Research, INFORMS, vol. 33(2), pages 249-262, April.
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    Cited by:

    1. Aner Sela, 2023. "Is there free riding in group contests?," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(2), pages 191-201, October.
    2. Sela, Aner, 2023. "Two-stage elimination games," Journal of Mathematical Economics, Elsevier, vol. 109(C).

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    More about this item

    Keywords

    Game theory; elimination tournaments; knockout tournaments;
    All these keywords.

    JEL classification:

    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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